Focal Mechanism and Focal Depth of the May 22，2016 MS4.6 Earthquake in Chaoyang，Liaoning1

INTRODUCTION

On May 22， 2016， at 17：08 p.m.， two earthquakes with MS4.6 （41.62°N， 120.10°E）and MS4.3 （41.63°N， 120.08°E） occurred successively in Chaoyang County， Liaoning Province.The epicentral distances of the two earthquakes are about 2km away from each other and about 30km from the urban area of Chaoyang.The earthquake occurred between the Chaoyang-Beipiao fault and Zhuluke-Dao'erdeng fault.

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The focal mechanism of an earthquake is an important parameter to describe the earthquake and plays an important role in the seismology research.The deep crustal stress field can be determined by using this parameter.The research methods of focal mechanism results include the classical P-wave initial motion method （Xu Zhonghuai et al.，1983； Yu Chunquan et al.，2009；Hu Xingping et al.，2008），P-wave and S-wave first motion method （Nakamura M.，2002），the amplitude ratio method of S-wave and P-wave（Liang Shanghong et al.，1984； Hu Xinliang et al.，2004；Hardebeck J.L.et al.，2002），the amplitude ratio method of the first motion（Snoke J.A，1984），and waveform inversion（Zhu Lupei et al.，1996；Minson S.E.et al.，2008）.At present， the CAP （Cut and Paste） method combining near-field and regional seismograms （Zhao Lianshe et al.， 1994； Zhu Lupei et al.，1996； Wei Shengji et al.，2009； Han Xiaoming et al.，2015）， by fitting Pnl waves and surface waves with different time-shifts reduces the dependence of the inversion on the wave velocity model.However，the method of full waveform inversion of seismic moment tensor（TDMT＿ISO） proposed by Minson S.E.et al. （2008） is more demanding for the wave velocity model.

Focal depth is one of the key parameters in seismology research and one of the parameters which is difficult to accurately measure at present.It is of great significance for geosciences research （Gao Yuan et al.，1997）， and its accurate determination will help to further understand the relationship between seismicity and faults（Galdeano C.S.et al.，1995）.The distribution of source location，seismogenic time and aftershock depth reflects the geometry of the seismogenic fault of the main shock，which can be used to explore the earthquake pregnant and the deep environment（Wu Changjiang et al.， 2004）.The depth of the seismogenic layer reflects the rheological properties of the medium and is an important indicator for determining the brittleductile transition of the seismogenic fault and the surrounding crustal crust（Stein S.et al.，1986）.Focal depth can also be determined by using the near-depth seismic facies sPL， sPg，sPmP and sPn （Gao Lixin et al.， 2007； Chong Jiajun et al.， 2010； Wang Dengwei， 2011）.Greensfelde R.W.（1965） proposed a method for determining the focal depth by using the time difference of the Pg-Pn wave recorded by the same station.Zhu Yuanqing et al.（1997） proposed a PTD method for determining the focal depth by using the Pn wave of the remote station and the time difference Pg-Pn of the Pg wave of the near station.Since the Pg wave of the near station and the Pn waves of the distance station are both first earthquake phases，the accuracy of the phase identification and the arrival picking up time are raised.

This paper uses a number of methods （P-wave first motion， the CAP and TDMT methods，the CAP， PTD and sPn-Pn methods） to study the focal mechanism results of the M4.6 earthquake in Chaoyang，Liaoning Province.The results of different methods are compared with each other to verify the reliability of the results and to reposition the medium and small earthquakes in the vicinity of the M4.6 earthquake （hypoDD method）.Focal mechanism results and focal depth are used to make a preliminary estimation of the seismogenic fault strike and the source zone stress characteristics of the Chaoyang M4.6 earthquake.

1 BACKGROUND AND DATA

On May 22， 2016， a magnitude 4.6 earthquake in Chaoyang County， Liaoning Province，occurred between the Chaoyang-Beipiao and Zhuluke-Berttemberl faults and the two faults were parallel to each other.The Chaoyang-Beipiao fault is located in Beipiao， Chaoyang City， Liaoning Province，and is about 200km long.It is a well-known inverse thrust fault in Liaoning Province and is an area where the earthquake in the Westem Liaoning area is relatively active.The Chaoyang-Beipiao fault is located in the Westem Liaoning uplift zone，and a series of NE-trending faults are formed along the northeast direction，such as the west side of the Jianshan fault and the Zhuluke-Dao'erdeng fault， among which a larger one is the Chaoyang-Beipiao fault （ Xia Huaikuan et al.， 1986）.

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Since the commencement of operation of the Digital Seismic Network in 2008，46 earthquakes were recorded in the source area （41.2°-42.4°N， 119.0°-120.0°E）.Fig.1 shows the epicenter and station distribution of the M4.6 earthquake （Fig.1（a））， the small earthquake distributions of the source area （Fig.1（b））， and the selected velocity model（Fig.1（c））.The selection model comes from Crust 2.0.As can be seen from Fig.1（b）， the small earthquakes around the M4.6 earthquake are mainly distributed in two parallel faults with distributions in both directions of NNE and NWW.

Fig.1 Earthquake，stations and velocity model

（a） Station distribution； （b） small earthquake distributions； （c） velocity model

2 PRINCIPLES AND METHODS

In this paper， we use the P-wave first motion， the CAP and TDMT methods to determine the focal mechanism results， and use the CAP， PTD and sPn-Pn methods to determine the focal depth.

2.1 The P-wave First Motion Method

In the CAP method calculation，13 waveform data items from better fitting stations are used.Fig.4（c） is the distribution of the stations using the CAP method.Fig.4（a） shows the waveform fitting，and most stations.The fitting correlation coefficients of three components of the surface waves of most stations are more than 95%，and the correlation coefficients of most body wave fitting are more than 70%.Fig.4（b） shows the variation of error with depth and the optimal focal mechanism results.The results show that the convergence of the inversion is good and the errordepth relationship is U-shaped.The error function at the focal depth of 17.1km is the minimum and the corresponding depth is the optimal depth.The focal mechanism results show little change near the optimal depth，indicating that the focal mechanism results are more stable.

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2.2 The CAP Method

The main idea of the CAP method is to divide the whole waveform of near-earthquakes into the P-wave （Pnl） and the surface wave （Sur） parts and give different weights to the three components of the two parts （Pnl does not have a tangential component） and invert them.Then the error function of the actual seismogram and the theoretical seismogram are calculated respectively.The grid search is carried out by using the grid search method within the given parameter space，and the focal mechanism results and focal depth are obtained when the relative error is minimum.According to the analysis of Zhu Lupei et al. （1996）， the CAP method uses the corrected absolute error of the epicentral distance as an error function，which is defined as

The PTD method uses the first arrival phases of different epicenter distances to convert Pn of the distance station from the beginning to the end to near station Pn at the arrival（the near station converted Pn at arrival time＝distance station Pn arrival time-Moho waves speed×epicenter distance difference）.When the epicentral distance is greater than the critical epicenter distance of Pn， the distant station Pn is converted into the near station Pn travel time， and the focal depth is determined according to the relationship between the Pg-Pn travel time difference and the depth.When the epicentral distance is less than the Pn critical epicenter distance，the distant station Pn is converted into the reference station Pn travel time，and the focal depth is calculated from the travel time difference between the Pg travel time and the reference station Pn travel time（Zhu Yuanqing et al.， 1990， 1997）.The travel time difference is defined by the critical epicenter distance of the Pn seismic phase.Fig.2（a） shows the relationship between travel time difference and epicentral distance at different focal depths.Fig.2（b） gives the relationship between time lag and depth when the different epicenter distance is different.By using Gaussian distribution to fit the frequency of multiple depth results，the optimal depth result is obtained with a 95%confidence interval error.

2.3 The TDMT Method

Dreger et al. （Dreger D.S.et al.，1993； Dreger D.S.，2003） proposed a TDMT （Time-Domain Moment Tensor）method for seismic moment tensor inversion in the time domain by using the wave three-component waveforms of the regional long-period body.This method selects longperiod recorded data of three-component seismic waveform data for two minutes and Pnl waveform data of the three-component bulk wave of the regional observation.The variance reduction value is used to determine the optimal focal depth and the focal mechanism.The variance reduction value VR is defined as

Among which， data is the measured data； synth is Green's function， summing all points of all stations.Before inversion calculation， the seismic data needs to be preprocessed.First， the observed waveforms are averaged and de-tilted.The deconvolved instrument transfers functions and records the integral.Then the waveforms are respectively rotated to tangential，radial and vertical directions； finally， the Butterworth band-pass filter is used to filter the observed data to the required long-period frequency band to suppress noise（Zoback M.L.，1992；Pasyanos M.E.et al.， 1996； Fukuyama E.et al.， 2000）.

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2.4 The PTD Method

Where u is the observed seismic displacement； s is the theoretical seismic displacement； r is the epicentral distance； r0is the reference epicentral distance set at 100km； p is the exponential factor， general body wave p＝1 and surface wave p＝0.5.

Fig.2 Pg， Pn ray path and travel time difference（Zhu Yuanqing et al.，1990）（a） Travel time difference-epicentral distance（the corresponding numbers on the curve are the corresponding depths（km））； （b） travel time difference-depth（the number is the different epicenter distance（km））； （c） ray path

2.5 The sPn-Pn Method

Seismic phase sPn is a recognizable seismic phase for the determination of focal depth at shallow distances（Δ ＜1000 km） and shallow earthquakes（within the earth's crust）.When the earthquake occurs within the crust，the SV component of the S-wave will be reflected after it enters the earth's surface and will be converted to a P-wave and then be incident on the Moho.When the angle of the incidence is the critical angle，a Pn wave is formed.Because it is converted by the S-wave，it is recorded as sPn wave.Based on the crustal model and the travel times of sPn and Pn，a linear relationship between focal depth and travel time can be derived（Gao Lixin et al.， 2007）.For the one-dimensional multi-velocity model， sPn-Pn travel time can be expressed as（Hong Xing et al.， 2006）.

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3 RESULTS AND ANALYSIS

3.1 Focal Mechanism Results

In order to obtain a more reliable focal depth，in addition to the above-mentioned depth results obtained by the CAP method，PTD and sPn-Pn methods are used to determine the focal depth of the Chaoyang M4.6 earthquake and the results of the three focal depths are compared in terms of consistency.

Fig.3 Data and results of the P-wave first motion method（a） Focal mechanism. × for upward first motion，o for downward first motion； （b） station distribution

According to the epicenter position，the azimuth and the deviation angle of the P-wave of the observed P-wave first motion station are observed.Based on the calculated P-wave first motion angle and deviation angle of the P-wave at the station，we mark the P-wave first motion symbols on the source sphere.We look for two focal sections of the focal mechanism.The focal sphere is divided into four equal areas，and minimize the difference between the observed P-wave first motion symbol and the P-wave first motion symbol predicted by the focal mechanism model（Wan Yongge， 2016）.

Where，h is the focal depth； Hnis the crustal thickness of the nth layer； vPmis the P-wave velocity of the Moho； the source is located in the ith layer，vPnand vSnare the P-wave and S-wave velocities of the nth layer respectively.

In the process of inversion by the TDMT method，stations with epicentral distances of 80km-400km are selected.After removing the stations with less than 60%variance reduction VR，5 stations with relatively high VR values are selected.Fig.5 shows the TDMT method inversion results.As seen from Fig.5，the average VR value is 78.5%.

Table 1 shows the inversion results of the three methods.It can be seen from Table 1 that the consistency between the CAP method and the TDMT method is high，and the focal mechanism gives two sets of possible section parameters.The specific seismogenic fault strike needs to be combined with the structural characteristics of the source area and the distribution of small earthquakes.

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Fig.4 Results and stations of the CAP method calculation

（a）Waveform fitting （Below the station codes are epicentral distance （km） and the station theory／observation P-wave first arrival difference.The red line is the theoretical seismogram.The black line is the observation of seismograms，with the first line below the waveform as the moving time of the theoretical seismogram relative to the observed seismograms， and the second as the correlation coefficient（%） between the two；（b）focal mechanism results and error-depth relationships （the number above the focal sphere is the moment magnitude from the depth calculation）； （c）station distribution

Table 1 Inversion results of focal mechanism of 3 methods

SectionⅠ SectionⅡMethod Strike／（°）Dip angle／（°）Slip angle／（°）Strike／（°）Dip angle／（°）Slip angle／（°）Moment magnitude P-wave first motion 232 85.5 -115.1 133.3 25.5 -10.6 ―CAP 235 82.6 -96.7 98.0 10.0 -48.0 4.5 TDMT 226 81.0 -95.0 76.0 10.0 -60.0 4.4

We used three methods to calculate the focal mechanism of the Chaoyang M4.6 earthquake，and the results obtained are consistent.The results of the CAP method and the TMDT method are highly consistent，based on the good velocity model.The reliability of the seismic moment tensor solution from the calculation of the theoretical seismogram is higher than that of the initial one，because the seismic waveform contains more source information than the initial one.

3.2 Focal Depth

Fig.3 shows the focal mechanism results for P-wave first motion and the distribution of used stations.We use the first motion information of 35 stations，and those of the Pg and Pn phases at the same time，including 10 initial Pg and 25 initial Pn.Section I of the focal mechanism goes to 232.9°with a dip angle of 85.5°and sliding angle of-115.1°.Section II heads for 133.3°with a dip angle of 25.5°and sliding angle of-10.6°.The P-axis direction is 118.3°with a dip angle of 44.0°.T-axis direction is 344.5°and the pitch angle is 35.5°.B-axis is 235.0°and the dip angle is 25.0°.The contradiction ratio of focal mechanism required is 0.084.As seen from Fig.3， the first motion direction is quadratically spatially distributed， the contradiction between the first motion and the result is relatively small，and the result is more reliable.

Fig.5 The TDMT results

（a）Waveform fitting （the solid line is the observed waveform， and the dashed line is the theoretical waveform）； （b）focal mechanism results； （c）station distribution

PTD method uses clear Pn， Pg travel time data，9 Pn travel times and 10 Pg travel times are used in total， and 90 depth results are obtained.Fig.6（d） shows the distribution of stations in use.Triangles indicate station positions using the Pn phase，and circles indicate station positions using the Pg phase.Fig.6（c） is a fitting graph of the results and frequency.The frequency distribution of the result is well coupled with the Gaussian distribution，indicating a reliable result with a depth of 18.2km and an error of 2.2km.Fig.6（a） is the comparison between the measured travel time difference and the theoretical travel time difference，and is a travel time difference-epicenter distance curve with a depth of 5km-35km in 5km steps.The thick line is the measured travel time difference curve corresponding to the depth result.The thin line is the theoretical travel time difference curve.Fig.6（b） is the residual distribution of travel time， in line with the normal distribution.

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The travel time difference between sPn and Pn phases is almost independent of the epicentral distance and is only affected by the focal depth.After the analysis of the seismic waveform Pn and sPn seismic phases of the Chaoyang M4.6 earthquake，six stations with relatively clear sPn seismic phases are selected，and the focal depth is calculated by using the sPn-Pn travel time difference.Fig.7（a） shows the Pn and Pg phase diagrams of six stations and sPn-Pn travel times of six stations.Fig.7（b） is based on the velocity model and sPn-Pn travel time difference-focal depth relationship from formula （3）.We can see that the sPn-Pn change with depth is more significant.The epicentral distances of the 6 stations used are 2.91°-6.26°.The travel time differences of sPn-Pn are 4.81s-5.42s，and the measured depths are 17.3km-19.5km with an average of 18.8km.

Fig.6 The PTD method using the inversion results of data and focal depth

（a） Travel time lag； （b） travel time error frequency； （c） Gaussian distribution fitting；（d） station distribution

Fig.7 Inversion results of sPn-Pn method and focal depth

（a）Vibration phase； （b）travel time difference-focal depth

Table 2 compares the focal depth results of the three methods.As seen from Table 2，the results of the PTD and sPn-Pn methods are the initial rupture depths and the CAP depths are the centroid depths of the earthquakes.For moderate earthquakes，the centroid depth is close to the initial rupture depth， so the results of the three methods are close to each other， and can be mutually verified.

Table 2 Results contrast of the focal depths

Method CAP PTD sPn-Pn Depth／km 17.1 18.2 18.8

4 CONCLUSION AND DISCUSSION

The focal mechanism results are consistent among the P-wave first motion，the CAP method and the TDMT method.They verify each other and obtain the two groups of section parameters：SectionI's strike is 226°-235°with a dip angle of 81.0°-85.5°， and a slip angle of-115.1°- -96.7°.SectionII's strike is 76°-133°with a dip angle of 10.0°-25.5°and s slip angle of-60.0°- -10.6°.Compared with the first motion method， the result of the CAP method and that of the TDMT method are more consistent.The seismic moment tensor solutions obtained by the CAP method and the TDMT method are more reliable because the seismic waveform contains more source information than the first motion.

Based on the focal mechanism results and the structural characteristics of source area and the small earthquake distributions，we can conclude that the seismogenic fault strike of the Chaoyang M4.6 earthquake is in the direction of NNE，and the focal mechanism is a normal fault type with a smaller left-lateral strike slip and the direction of the main pressure force is NWW.The NEEE stress field is formed by the interaction of the Pacific plate，the Philippine plate and the Indian plate in northeastern China，and the subduction stress field of the present Pacific plate plays a leading role （Wang Zhaoguo et al.， 2009）.The NEE tectonic belt in western Liaoning is dominated by the crustal tectonic environment in the Mesozoic Era and is mainly connected with the torsional of crustal faults，and the moderately strong earthquakes and the successive fault activities that control the basins（Lei Qingqing et al.，2008）.The Mesozoic tectonics in western Liaoning are generally NE-NNE and formed by mountains （paleohighs） and broad low-lying basins （Jiang Shu'e et al.， 2009）.The presence of the Chaoyang-Beipiao anti-overtopping fault strongly proves that the tectonic movement was quite intense during the Mesozoic in western Liaoning and its tectonic stress field is NW-SE horizontal compressive stress.Under the action of this stress field，a basic tectonic pattern is formed in western Liaoning.A series of NE-trending uplifts and depressions are arranged in phases with NE-trending faults and the Chaoyang-Beipiao fault has declining activity characteristics （Xia Huaikuan et al.， 1986）.The Chaoyang M4.6 earthquake was located in the depression between the two faults.According to the structural characteristics，this area is mainly characterized by the vertical movements under the vertical force.The direction of the main pressure force of the earthquake is in line with the stress characteristics in western Liaoning.The focal mechanism section of the NNE direction is more in line with the tectonic framework of the area.Since the Cenozoic，a new normal fault has been formed in Laohushan 50km northwest of Chaoyang County with a 34°section heading NW and a dip angle of 68°（Xia Huaikuan et al.， 1986）.The location and structure of the fault are similar to the focal mechanism results of the Chaoyang M4.6 earthquake and could be the seismogenic fault strike of this earthquake.

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